12z^2-16z+5=0

Solution for 12z^2-16z+5=0 equation:

Simplifying
12z2 + -16z + 5 = 0

Reorder the terms:
5 + -16z + 12z2 = 0

Solving
5 + -16z + 12z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -2z)(5 + -6z) = 0

Subproblem 1
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Subproblem 2
Set the factor '(5 + -6z)' equal to zero and attempt to solve:

Simplifying
5 + -6z = 0

Solving
5 + -6z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -6z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6z = 0 + -5
-6z = 0 + -5

Combine like terms: 0 + -5 = -5
-6z = -5

Divide each side by '-6'.
z = 0.8333333333

Simplifying
z = 0.8333333333
Solution
z = {0.5, 0.8333333333}